1. Field of the Invention
The present invention relates generally to inertial navigation systems, and specifically to a system and method for improving the accuracy of pressure altitude determinations in an inertial navigation system.
2. Description of Related Art
Inertial navigation systems in aircrafts have typically employed a accelerometers to provide position information to a navigation computer. It is well known that the vertical position (altitude) of the aircraft can be determined from a measured acceleration in the vertical direction by performing a double time integration of the measured vertical acceleration.
The double integration of acceleration in the vertical direction is unstable as acceleration bias can lead to exponential growth in the computed altitude, causing the estimated altitude calculation to have unbounded error due to several factors. First, any vertical acceleration measurement errors from the accelerometers are directly integrated in subsequent calculations to cause both vertical velocity and vertical position error. Second, in order to obtain the actual value for vertical acceleration from the measurement taken by the accelerometer, the effects of gravity must be subtracted from the vertical acceleration measurement. Erroneous acceleration measurements will cause incorrect values for gravity to be subtracted from the measured acceleration, which further compounds the error in the altitude determination causing an even faster growth in the altitude error. Thus, inertial navigation systems relying upon the integration of acceleration measurements to obtain an estimation of altitude are unstable systems.
To provide a more stable inertial navigation system, external references have been used either alone or in combination with inertial measurements to compute estimations of altitude. For instance, a barometric altimeter is a well known device for providing altitude information as a function of the value of barometric pressure based on the direct relationship between pressure and altitude. Barometric altitude, also known as pressure altitude, is determined as a function of pressure based on the standard day model for the atmosphere: ##EQU1##
where S is the pressure altitude, K.sub.1 =44.342 [km], K.sub.2 =0.190263, K.sub.3 =45.395 [km], K.sub.4 =14.605 [km], P.sub.0 =1013.25 [mb], and P.sub.B =226.32 [mb]. Since the barometric altitude determination is stable, it is typically used in a variety of mechanizations to aid (i.e., bound) the inertial vertical loop. The standard day model for the atmosphere utilizes several fixed values which were derived to represent the average atmospheric conditions over a broad range of possible atmospheric conditions. Atmospheric conditions encountered by an aircraft usually differ from these average conditions defined by the standard day model, resulting in large inertial altitude and velocity errors when measured pressure values are simply inserted into the standard day model. Thus, the pressure altitude estimated from the standard day model and true altitude can differ significantly.
Differences between the calculated pressure altitude and true altitude are a result of the pressure altitude being based on the standard atmosphere, whereas atmospheric conditions encountered by an aircraft are usually nonstandard. A more accurate estimate for altitude can be obtained by accounting for nonstandard atmospheric conditions. One technique, known as the Blanchard altitude, was developed to compute a reference altitude based on a dynamic mathematical model of the nonstandard atmosphere rather than the assumed standard atmosphere model. The Blanchard altitude is a dynamically corrected altitude reference computed by numerically integrating the physical relationship between temperature, pressure, and altitude, where the Blanchard altitude (Z) is defined by the following equation: ##EQU2##
where R* is the universal gas constant, M is an approximation for the molecular weight of air, g is the acceleration due to gravity, T is the temperature, and P is the pressure. The calculation of the Blanchard altitude is described in an article "A New Algorithm for Computing Inertial Altitude and Vertical Velocity," by R. L. Blanchard, published in IEEE Trans. on Aerospace and Electronic Systems, Vol. AES-7, No. 6, November 1971. The disclosure of this article is hereby incorporated by reference into the present application.
The relationship set forth in the Blanchard altitude equation is only valid in a region of air having a consistent relationship between pressure and altitude as well as temperature and altitude. The Blanchard altitude calculation assumes a frozen atmosphere having a constant density of air. However, an aircraft will encounter separate regions of air possessing different respective atmospheric conditions during its flight path. The Blanchard altitude calculation does not account for changes in atmospheric conditions between different regions of air. Thus, assumptions made about the atmospheric conditions in one region of air will not necessarily apply to atmospheric conditions in other regions of air, which could cause substantial differences between the estimated Blanchard altitude and the true altitude of the aircraft. Furthermore, since the Blanchard altitude is calculated using an integration of the physical relationship between temperature, pressure, and altitude, the Blanchard altitude is typically computed numerically by summing estimates of the change in altitude over time as computed using this physical relationship. Thus, any errors in the temperature or pressure measurements are summed into the Blanchard altitude estimation, and these errors will always remain present in the Blanchard altitude estimation and build upon one another in all future altitude estimations. These erroneous measurements can be another cause of differences between the estimated Blanchard altitude and the true altitude of the aircraft.
Thus, there is clearly a need for a system and method for more accurately measuring altitude in inertial navigation systems which accounts for changes in atmospheric conditions encountered during various stages of the flight path of an aircraft. Furthermore, there is a need for a system and method for more accurately measuring altitude in an inertial navigation system which limits the effects of erroneous measurements used in calculating altitude estimations.